Intensity of the incident light

[vrobins1]

Homework Statement

Unpolarized light is incident on a system of three polarizers. The second polarizer is oriented at an angle of 33.0° with respect to the first and the third is oriented at an angle of 45.0° with respect to the first. If the light that emerges from the system has an intensity of 2.3 W/m2, what is the intensity of the incident light?

Homework Equations

I_out=I_incos²$$\theta$$

The Attempt at a Solution

I know that after I₀ passes through the first polarizer, it is 1/2I₀. After it passes through the second, I thought it would be 1/2I₀cos²(33), and after it passes through the third, 1/2I₀cos²(33)cos²(45).
This would all equal 2.3, which I was given.
So I set up my final equation as:
1/2I₀cos²(33)cos²(45) = 2.3, or
I₀= 2.3 / (1/2cos²(33)cos²(45).

I solved and got 13.08, but that is incorrect. Can anyone offer any insight? Thanks.

 

[Redbelly98]

For the third polarizer, use the angle between it and the second polarizer.

45° is the angle between the third and first polarizer.